ID: de39858a
(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)
Comment: Work with one piece of information at a time. Plug in what makes sense to get the ball rolling. In my view, there are a few components that make this question more challenging:
1) A graphing calculator such as Desmos will be of little use, since there are two additional unknowns besides the typical x and y.
2) There are a lot of steps involved.
3) The fraction 325/36 is not the easiest number to work with.
4) There is a negative exponent.
5) The question is not asking about the value of a or b alone, which could lead to a simple substitution of the answer choices, but about their product. (A good trap answer would have included, say, the value of a.)
Method 1: Any time you can set one unknown to 0, it is probably worth exploring the effects of doing so. Substitute the values from the ordered pair (0, 10) into the given function.
h(x) = a^x + b
(10) = a^(0) + b
10 = 1 + b
9 = b
Now, substitute the other set of numbers to isolate a.
(325/36) = a^(-2) + 9
325/36 - 324/36 = 1/a^2
1/36 = 1/a^2
+/- 6 = a
Because we are told that a and b are positive constants, a = 6. Finally, the product ab is (6)(9), or 54. The correct answer is (C).
Method 2: You could set up an equation using Desmos and add sliders for an and b, but with the numbers involved, it probably would not be an approach worth pursuing. I imagine it would take most students over three minutes to get even close to an answer before guessing.
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